Subgroups — #30652932

Order 16256.

1038 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550628	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550626	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550621	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550620	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550586	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550580	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550567	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550565	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550556	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550554	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550551	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550550	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550528	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550524	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550519	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550515	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550503	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550501	C₂	1	1	yes	maximal, characteristic, complemented
19	#22550496	C₂	1	1	yes	maximal, characteristic, complemented
20	#22550472	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550469	C₂	1	1	yes	maximal, characteristic, complemented
22	#22550468	C₂	1	1	yes	maximal, characteristic, complemented
23	#22550467	C₂	1	1	yes	maximal, characteristic, complemented
24	#22550467	C₂	1	1	yes	maximal, characteristic, complemented
25	#22550460	C₂	1	1	yes	maximal, characteristic, complemented
26	#22550451	C₂	1	1	yes	maximal, characteristic, complemented
27	#22550446	C₂	1	1	yes	maximal, characteristic, complemented
28	#22550385	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂²⋊Q₈×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#542×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#14523249	C₂²	1	1	yes	characteristic
33	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14523247	C₂²	1	1	yes	characteristic
35	C₂×Q₈×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
38	#16861209	C₂²	1	1	yes	characteristic, complemented
39	#16861208	C₂²	1	1	yes	characteristic, complemented
40	#16861207	C₂²	1	1	yes	characteristic, complemented
41	#16861207	C₂²	1	1	yes	characteristic, complemented
42	#16861207	C₂²	1	1	yes	characteristic, complemented
43	#16861204	C₂²	1	1	yes	characteristic, complemented
44	#16861204	C₂²	1	1	yes	characteristic, complemented
45	#16861203	C₂²	1	1	yes	characteristic, complemented
46	#16861203	C₂²	1	1	yes	characteristic, complemented
47	#16861202	C₂²	1	1	yes	characteristic, complemented
48	#16861202	C₂²	1	1	yes	characteristic, complemented
49	#16861202	C₂²	1	1	yes	characteristic, complemented
50	#16861202	C₂²	1	1	yes	characteristic, complemented
51	#16861202	C₂²	1	1	yes	characteristic, complemented
52	#16861202	C₂²	1	1	yes	characteristic, complemented
53	#16861201	C₂²	1	1	yes	characteristic, complemented
54	#16861201	C₂²	1	1	yes	characteristic, complemented
55	#16861201	C₂²	1	1	yes	characteristic, complemented
56	#16861201	C₂²	1	1	yes	characteristic, complemented
57	#16861200	C₂²	1	1	yes	characteristic, complemented
58	#16861200	C₂²	1	1	yes	characteristic, complemented
59	#16861199	C₂²	1	1	yes	characteristic, complemented
60	#16861199	C₂²	1	1	yes	characteristic, complemented
61	#16861199	C₂²	1	1	yes	characteristic, complemented
62	#16861199	C₂²	1	1	yes	characteristic, complemented
63	#16861198	C₂²	1	1	yes	characteristic, complemented
64	#16861197	C₂²	1	1	yes	characteristic, complemented
65	#16861196	C₂²	1	1	yes	characteristic, complemented
66	#16861195	C₂²	1	1	yes	characteristic
67	#16861195	C₂²	1	1	yes	characteristic, complemented
68	#16861194	C₂²	1	1	yes	characteristic
69	#16861194	C₂²	1	1	yes	characteristic
70	#16861194	C₂²	1	1	yes	characteristic
71	#16861194	C₂²	1	1	yes	characteristic
72	#16861194	C₂²	1	1	yes	characteristic, complemented
73	#16861194	C₂²	1	1	yes	characteristic, complemented
74	#16861194	C₂²	1	1	yes	characteristic, complemented
75	#16861193	C₂²	1	1	yes	characteristic
76	#16861193	C₂²	1	1	yes	characteristic, complemented
77	#16861193	C₂²	1	1	yes	characteristic, complemented
78	#16861192	C₂²	1	1	yes	characteristic
79	#16861192	C₂²	1	1	yes	characteristic, complemented
80	#16861191	C₂²	1	1	yes	characteristic
81	#16861191	C₂²	1	1	yes	characteristic
82	#16861191	C₂²	1	1	yes	characteristic
83	#16861191	C₂²	1	1	yes	characteristic
84	#16861191	C₂²	1	1	yes	characteristic
85	#16861191	C₂²	1	1	yes	characteristic, complemented
86	#16861191	C₂²	1	1	yes	characteristic, complemented
87	#16861191	C₂²	1	1	yes	characteristic, complemented
88	#16861191	C₂²	1	1	yes	characteristic, complemented
89	#16861191	C₂²	1	1	yes	characteristic, complemented
90	#16861191	C₂²	1	1	yes	characteristic, complemented
91	#16861190	C₂²	1	1	yes	characteristic
92	#16861190	C₂²	1	1	yes	characteristic
93	#16861190	C₂²	1	1	yes	characteristic, complemented
94	#16861189	C₂²	1	1	yes	characteristic
95	#16861189	C₂²	1	1	yes	characteristic, complemented
96	#16861189	C₂²	1	1	yes	characteristic, complemented
97	#16861188	C₂²	1	1	yes	characteristic, complemented
98	#16861188	C₂²	1	1	yes	characteristic, complemented
99	#16861187	C₂²	1	1	yes	characteristic
100	#16861187	C₂²	1	1	yes	characteristic
101	#16861187	C₂²	1	1	yes	characteristic
102	#16861187	C₂²	1	1	yes	characteristic
103	#16861187	C₂²	1	1	yes	characteristic
104	#16861187	C₂²	1	1	yes	characteristic, complemented
105	#16861187	C₂²	1	1	yes	characteristic, complemented
106	#16861187	C₂²	1	1	yes	characteristic, complemented
107	#16861187	C₂²	1	1	yes	characteristic, complemented
108	#16861187	C₂²	1	1	yes	characteristic, complemented
109	#16861187	C₂²	1	1	yes	characteristic, complemented
110	#16861186	C₂²	1	1	yes	characteristic, complemented
111	#16861186	C₂²	1	1	yes	characteristic, complemented
112	#16861186	C₂²	1	1	yes	characteristic, complemented
113	#16861186	C₂²	1	1	yes	characteristic, complemented
114	#16861186	C₂²	1	1	yes	characteristic, complemented
115	#16861186	C₂²	1	1	yes	characteristic, complemented
116	#16861186	C₂²	1	1	yes	characteristic, complemented
117	#16861186	C₂²	1	1	yes	characteristic, complemented
118	#16861186	C₂²	1	1	yes	characteristic, complemented
119	#16861185	C₂²	1	1	yes	characteristic
120	#16861185	C₂²	1	1	yes	characteristic
121	#16861185	C₂²	1	1	yes	characteristic
122	#16861185	C₂²	1	1	yes	characteristic, complemented
123	#16861185	C₂²	1	1	yes	characteristic, complemented
124	#16861185	C₂²	1	1	yes	characteristic, complemented
125	#16861182	C₂²	1	1	yes	characteristic
126	#16861182	C₂²	1	1	yes	characteristic
127	#16861182	C₂²	1	1	yes	characteristic
128	#16861182	C₂²	1	1	yes	characteristic
129	#16861182	C₂²	1	1	yes	characteristic, complemented
130	#16861181	C₂²	1	1	yes	characteristic
131	#16861181	C₂²	1	1	yes	characteristic, complemented
132	#16861181	C₂²	1	1	yes	characteristic, complemented
133	#16861180	C₂²	1	1	yes	characteristic
134	#16861179	C₂²	1	1	yes	characteristic
135	#16861179	C₂²	1	1	yes	characteristic
136	#16861177	C₂²	1	1	yes	characteristic
137	#16861177	C₂²	1	1	yes	characteristic
138	#16861174	C₂²	1	1	yes	characteristic, complemented
139	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
140	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
141	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
142	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
143	#16861171	C₂²	1	1	yes	characteristic, complemented
144	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
145	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
147	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
148	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
150	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	#16861167	C₂²	1	1	yes	characteristic
153	#16861167	C₂²	1	1	yes	characteristic, complemented
154	#16861166	C₂²	1	1	yes	characteristic
155	#16861166	C₂²	1	1	yes	characteristic, complemented
156	#16861166	C₂²	1	1	yes	characteristic, complemented
157	#16861166	C₂²	1	1	yes	characteristic, complemented
158	C₂×Dic₁₂₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
160	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
161	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
164	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
165	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
173	#126×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
174	#126×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
175	#124×C₁₂₇	C₂²	1	1	yes	characteristic
176	#124×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
177	#124×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
178	#123×C₁₂₇	C₂²	1	1	yes	characteristic
179	#123×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
181	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
183	#121×C₁₂₇	C₂²	1	1	yes	characteristic
184	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
186	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
188	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
189	#14523249	—	4	2	no	—
190	#14523248	—	4	2	no	—
191	#14523247	—	4	2	no	—
192	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
193	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
194	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
195	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
196	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
197	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
198	Q₈×D₁₂₇	—	4	2	no	—
199	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
200	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
201	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
202	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
211	D₄×D₁₂₇	—	4	2	no	—
212	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
213	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
214	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
215	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₁₂₇	—	4	2	no	—
217	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
245	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
268	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
269	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
270	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
271	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
272	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
283	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
307	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
308	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
309	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
315	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
344	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
345	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
346	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
347	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
348	C₂²×D₁₂₇	—	2	2	no	—
349	C₂²×D₁₂₇	—	2	2	no	—
350	C₂²×D₁₂₇	—	2	2	no	—
351	C₂²×D₁₂₇	—	4	1	no	—
352	C₂²×D₁₂₇	—	4	1	no	—
353	C₂²×D₁₂₇	—	4	1	no	—
354	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
356	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
357	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
358	Dic₂₅₄	—	4	1	no	—
359	Dic₂₅₄	—	4	1	no	—
360	Dic₂₅₄	—	4	1	no	—
361	Dic₂₅₄	—	4	1	no	—
362	Dic₂₅₄	—	4	1	no	—
363	Dic₂₅₄	—	4	1	no	—
364	D₅₀₈	—	2	2	no	—
365	D₅₀₈	—	2	2	no	—
366	D₅₀₈	—	2	2	no	—
367	D₅₀₈	—	4	1	no	—
368	C₂²⋊D₁₂₇	—	2	2	no	—
369	C₂²⋊D₁₂₇	—	2	2	no	—
370	C₂²⋊D₁₂₇	—	2	2	no	—
371	C₂²⋊D₁₂₇	—	4	1	no	—
372	C₂²⋊D₁₂₇	—	4	1	no	—
373	C₂²⋊D₁₂₇	—	4	1	no	—
374	C₂²⋊D₁₂₇	—	4	1	no	—
375	C₂²⋊D₁₂₇	—	4	1	no	—
376	C₂×Dic₁₂₇	—	4	1	no	—
377	C₂×Dic₁₂₇	—	4	1	no	—
378	C₂×Dic₁₂₇	—	4	1	no	—
379	C₂×Dic₁₂₇	—	4	1	no	—
380	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
392	C₄×D₁₂₇	—	2	2	no	—
393	C₄×D₁₂₇	—	2	2	no	—
394	C₄×D₁₂₇	—	2	2	no	—
395	C₄×D₁₂₇	—	2	2	no	—
396	C₄×D₁₂₇	—	2	2	no	—
397	C₄×D₁₂₇	—	4	1	no	—
398	C₄×D₁₂₇	—	4	1	no	—
399	C₄×D₁₂₇	—	4	1	no	—
400	C₄×D₁₂₇	—	4	1	no	—
401	C₄×D₁₂₇	—	4	1	no	—
402	C₄×D₁₂₇	—	4	1	no	—
403	C₄×D₁₂₇	—	4	1	no	—
404	C₄×D₁₂₇	—	4	1	no	—
405	C₄×D₁₂₇	—	4	1	no	—
406	C₄×D₁₂₇	—	4	1	no	—
407	C₄×D₁₂₇	—	4	1	no	—
408	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
409	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
410	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
411	Q₈×C₁₂₇	—	4	1	no	—
412	Q₈×C₁₂₇	—	4	1	no	—
413	Q₈×C₁₂₇	—	4	1	no	—
414	D₄×C₁₂₇	—	4	1	no	—
415	D₄×C₁₂₇	—	4	1	no	—
416	D₄×C₁₂₇	—	4	1	no	—
417	C₂×C₄×C₁₂₇	—	4	1	no	—
418	C₂×C₄×C₁₂₇	—	4	1	no	—
419	C₂×C₄×C₁₂₇	—	4	1	no	—
420	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
426	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
427	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
428	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
431	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
432	C₂²×C₁₂₇	—	2	1	no	—
433	C₂²×C₁₂₇	—	2	1	no	—
434	C₂²×C₁₂₇	—	2	1	no	—
435	C₂²×C₁₂₇	—	2	1	no	—
436	C₂²×C₁₂₇	—	2	1	no	—
437	C₂²×C₁₂₇	—	2	1	no	—
438	C₂²×C₁₂₇	—	2	1	no	—
439	C₂²×C₁₂₇	—	2	1	no	—
440	C₂²×C₁₂₇	—	2	1	no	—
441	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
442	C₂×D₁₂₇	—	2	1	no	—
443	C₂×D₁₂₇	—	2	1	no	—
444	C₂×D₁₂₇	—	2	1	no	—
445	C₂×D₁₂₇	—	2	1	no	—
446	C₂×D₁₂₇	—	2	1	no	—
447	C₂×D₁₂₇	—	2	1	no	—
448	C₂×D₁₂₇	—	2	1	no	—
449	C₂×D₁₂₇	—	2	1	no	—
450	C₂×D₁₂₇	—	2	1	no	—
451	C₂×D₁₂₇	—	2	1	no	—
452	C₂×D₁₂₇	—	4	4	no	—
453	C₂×D₁₂₇	—	8	2	no	—
454	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	—
455	C₂×D₁₂₇	2₋¹⁺⁴	1	2	yes	—
456	C₄×C₁₂₇	—	2	1	no	—
457	C₄×C₁₂₇	—	2	1	no	—
458	C₄×C₁₂₇	—	2	1	no	—
459	C₄×C₁₂₇	—	2	1	no	—
460	C₄×C₁₂₇	—	2	1	no	—
461	C₄×C₁₂₇	—	2	1	no	—
462	C₄×C₁₂₇	—	2	1	no	—
463	C₄×C₁₂₇	—	2	1	no	—
464	C₄×C₁₂₇	—	2	1	no	—
465	C₄×C₁₂₇	—	2	1	no	—
466	C₄×C₁₂₇	—	2	1	no	—
467	C₄×C₁₂₇	—	2	1	no	—
468	Dic₁₂₇	—	2	1	no	—
469	Dic₁₂₇	—	2	1	no	—
470	Dic₁₂₇	—	2	1	no	—
471	Dic₁₂₇	—	2	1	no	—
472	Dic₁₂₇	—	2	1	no	—
473	Dic₁₂₇	—	2	1	no	—
474	Dic₁₂₇	—	2	1	no	—
475	Dic₁₂₇	—	2	1	no	—
476	Dic₁₂₇	—	2	1	no	—
477	Dic₁₂₇	—	2	1	no	—
478	Dic₁₂₇	—	2	1	no	—
479	Dic₁₂₇	—	2	1	no	—
480	C₂×C₁₂₇	—	4	1	no	—
481	C₂×C₁₂₇	—	4	1	no	—
482	C₂×C₁₂₇	—	4	1	no	—
483	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
484	C₂×C₁₂₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂×C₁₂₇	#585	1	1	yes	characteristic
486	D₁₂₇	—	2	2	no	—
487	D₁₂₇	—	2	2	no	—
488	D₁₂₇	—	4	1	no	—
489	D₁₂₇	—	4	1	no	—
490	#3535	—	127	1	no	maximal, Sylow
491	C₁₂₇	#3535	1	1	yes	characteristic, complemented, Sylow
492	#563	—	127	1	no	—
493	#563	—	127	1	no	—
494	#562	—	127	1	no	—
495	#562	—	127	1	no	—
496	#554	—	127	1	no	—
497	#554	—	127	1	no	—
498	#552	—	127	1	no	—
499	#552	—	127	1	no	—
500	#551	—	127	1	no	—
501	#551	—	127	1	no	—
502	#551	—	127	1	no	—
503	#551	—	127	1	no	—
504	#547	—	127	1	no	—
505	#547	—	127	1	no	—
506	#546	—	127	1	no	—
507	#546	—	127	1	no	—
508	#544	—	127	1	no	—
509	#543	—	127	1	no	—
510	#542	—	127	1	no	—
511	#542	D₁₂₇	1	1	yes	characteristic, complemented
512	#539	—	127	1	no	—
513	#539	—	127	1	no	—
514	#539	—	127	1	no	—
515	#539	—	127	1	no	—
516	#539	—	127	1	no	—
517	#538	—	127	1	no	—
518	#536	—	127	1	no	—
519	#536	—	127	1	no	—
520	#525	—	127	1	no	—
521	C₂×#123	—	127	1	no	—
522	C₂×C₂²⋊Q₈	—	127	1	no	—
523	C₂×#41	—	127	1	no	—
524	C₂×#41	—	127	1	no	—
525	C₂×#41	—	127	1	no	—
526	C₂²×Q₈	—	127	1	no	—
527	C₂²×D₄	—	127	1	no	—
528	C₂³×C₄	—	127	1	no	—
529	C₄⋊Q₈	—	127	1	no	—
530	C₄⋊Q₈	—	127	1	no	—
531	C₄⋊Q₈	—	127	1	no	—
532	C₄⋊Q₈	—	127	1	no	—
533	C₄⋊Q₈	—	127	1	no	—
534	C₄⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
535	#126	—	127	1	no	—
536	#126	—	127	1	no	—
537	#126	—	127	1	no	—
538	#126	—	127	1	no	—
539	#126	—	127	1	no	—
540	#126	—	127	1	no	—
541	#126	—	127	1	no	—
542	#126	—	127	1	no	—
543	#126	—	127	1	no	—
544	#126	—	127	1	no	—
545	#126	C₂×D₁₂₇	1	1	yes	characteristic, complemented
546	#126	C₂×D₁₂₇	1	1	yes	characteristic, complemented
547	#125	—	127	1	no	—
548	#125	—	127	1	no	—
549	#125	—	127	1	no	—
550	#125	—	127	1	no	—
551	#125	—	127	1	no	—
552	#125	—	127	1	no	—
553	#125	—	127	1	no	—
554	#125	—	127	1	no	—
555	#125	—	127	1	no	—
556	#125	—	127	1	no	—
557	#124	—	127	1	no	—
558	#124	—	127	1	no	—
559	#124	—	127	1	no	—
560	#124	—	127	1	no	—
561	#124	—	127	1	no	—
562	#124	C₂×D₁₂₇	1	1	yes	characteristic
563	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
564	#124	C₂×D₁₂₇	1	1	yes	characteristic, complemented
565	#123	—	127	1	no	—
566	#123	—	127	1	no	—
567	#123	—	127	1	no	—
568	#123	—	127	1	no	—
569	#123	—	127	1	no	—
570	#123	—	127	1	no	—
571	#123	—	127	1	no	—
572	#123	—	127	1	no	—
573	#123	—	127	1	no	—
574	#123	—	127	1	no	—
575	#123	—	127	1	no	—
576	#123	—	127	1	no	—
577	#123	—	127	1	no	—
578	#123	—	127	1	no	—
579	#123	—	127	1	no	—
580	#123	—	127	1	no	—
581	#123	—	127	1	no	—
582	#123	—	127	1	no	—
583	#123	—	127	1	no	—
584	#123	—	127	1	no	—
585	#123	—	127	1	no	—
586	#123	—	127	1	no	—
587	#123	—	127	1	no	—
588	#123	—	127	1	no	—
589	#123	—	127	1	no	—
590	#123	—	127	1	no	—
591	#123	C₂×D₁₂₇	1	1	yes	characteristic
592	#123	C₂×D₁₂₇	1	1	yes	characteristic, complemented
593	C₂²⋊Q₈	—	127	1	no	—
594	C₂²⋊Q₈	—	127	1	no	—
595	C₂²⋊Q₈	—	127	1	no	—
596	C₂²⋊Q₈	—	127	1	no	—
597	C₂²⋊Q₈	—	127	1	no	—
598	C₂²⋊Q₈	—	127	1	no	—
599	C₂²⋊Q₈	—	127	1	no	—
600	C₂²⋊Q₈	—	127	1	no	—
601	C₂²⋊Q₈	—	127	1	no	—
602	C₂²⋊Q₈	—	127	1	no	—
603	C₂²⋊Q₈	—	127	1	no	—
604	C₂²⋊Q₈	—	127	1	no	—
605	C₂²⋊Q₈	—	127	1	no	—
606	C₂²⋊Q₈	—	127	1	no	—
607	C₂²⋊Q₈	—	127	1	no	—
608	C₂²⋊Q₈	—	127	1	no	—
609	C₂²⋊Q₈	—	127	1	no	—
610	C₂²⋊Q₈	—	127	1	no	—
611	C₂²⋊Q₈	—	127	1	no	—
612	C₂²⋊Q₈	—	127	1	no	—
613	C₂²⋊Q₈	—	127	1	no	—
614	C₂²⋊Q₈	—	127	1	no	—
615	C₂²⋊Q₈	—	127	1	no	—
616	C₂²⋊Q₈	—	127	1	no	—
617	C₂²⋊Q₈	—	127	1	no	—
618	C₂²⋊Q₈	—	127	1	no	—
619	C₂²⋊Q₈	—	127	1	no	—
620	C₂²⋊Q₈	—	127	1	no	—
621	C₂²⋊Q₈	—	127	1	no	—
622	C₂²⋊Q₈	—	127	1	no	—
623	C₂²⋊Q₈	—	127	1	no	—
624	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
625	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
626	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
627	#121	—	127	1	no	—
628	#121	—	127	1	no	—
629	#121	—	127	1	no	—
630	#121	—	127	1	no	—
631	#121	—	127	1	no	—
632	#121	—	127	1	no	—
633	#121	—	127	1	no	—
634	#121	—	127	1	no	—
635	#121	—	127	1	no	—
636	#121	C₂×D₁₂₇	1	1	yes	characteristic
637	#120	—	127	1	no	—
638	#120	—	127	1	no	—
639	#120	—	127	1	no	—
640	#120	—	127	1	no	—
641	C₄×Q₈	—	127	1	no	—
642	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
643	C₄×D₄	—	127	1	no	—
644	C₄×D₄	—	127	1	no	—
645	C₄×D₄	—	127	1	no	—
646	C₄×D₄	—	127	1	no	—
647	C₄×D₄	—	127	1	no	—
648	C₄×D₄	—	127	1	no	—
649	C₄×D₄	—	127	1	no	—
650	C₄×D₄	—	127	1	no	—
651	C₄×D₄	—	127	1	no	—
652	C₄×D₄	—	127	1	no	—
653	C₄×D₄	—	127	1	no	—
654	C₄×D₄	—	127	1	no	—
655	C₄×D₄	—	127	1	no	—
656	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
657	#117	—	127	1	no	—
658	#117	—	127	1	no	—
659	#117	—	127	1	no	—
660	#117	—	127	1	no	—
661	#117	—	127	1	no	—
662	#117	—	127	1	no	—
663	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
664	C₂×C₄⋊C₄	—	127	1	no	—
665	C₂×C₄⋊C₄	—	127	1	no	—
666	C₂×C₄⋊C₄	—	127	1	no	—
667	C₂×C₄⋊C₄	—	127	1	no	—
668	C₂×C₄⋊C₄	—	127	1	no	—
669	C₂×C₄⋊C₄	—	127	1	no	—
670	C₂×C₄⋊C₄	—	127	1	no	—
671	C₂×C₂²⋊C₄	—	127	1	no	—
672	C₂×C₂²⋊C₄	—	127	1	no	—
673	C₂×C₂²⋊C₄	—	127	1	no	—
674	C₂×C₂²⋊C₄	—	127	1	no	—
675	C₂×C₂²⋊C₄	—	127	1	no	—
676	C₂×C₂²⋊C₄	—	127	1	no	—
677	C₂×C₂²⋊C₄	—	127	1	no	—
678	C₂⁴	—	127	1	no	—
679	C₂⁴	—	127	1	no	—
680	#41	—	508	2	no	—
681	#41	—	508	2	no	—
682	#41	—	508	2	no	—
683	C₂×Q₈	—	127	1	no	—
684	C₂×Q₈	—	127	1	no	—
685	C₂×Q₈	—	127	1	no	—
686	C₂×Q₈	—	127	1	no	—
687	C₂×Q₈	—	127	1	no	—
688	C₂×Q₈	—	127	1	no	—
689	C₂×Q₈	—	508	2	no	—
690	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
691	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
692	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
693	C₂×D₄	—	127	1	no	—
694	C₂×D₄	—	127	1	no	—
695	C₂×D₄	—	127	1	no	—
696	C₂×D₄	—	127	1	no	—
697	C₂×D₄	—	127	1	no	—
698	C₂×D₄	—	127	1	no	—
699	C₂×D₄	—	127	1	no	—
700	C₂×D₄	—	127	1	no	—
701	C₂×D₄	—	127	1	no	—
702	C₂×D₄	—	127	1	no	—
703	C₂×D₄	—	127	1	no	—
704	C₂×D₄	—	127	1	no	—
705	C₂×D₄	—	508	2	no	—
706	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
707	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
708	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
709	C₂²×C₄	—	127	1	no	—
710	C₂²×C₄	—	127	1	no	—
711	C₂²×C₄	—	127	1	no	—
712	C₂²×C₄	—	127	1	no	—
713	C₂²×C₄	—	127	1	no	—
714	C₂²×C₄	—	127	1	no	—
715	C₂²×C₄	—	127	1	no	—
716	C₂²×C₄	—	127	1	no	—
717	C₂²×C₄	—	127	1	no	—
718	C₂²×C₄	—	127	1	no	—
719	C₂²×C₄	—	127	1	no	—
720	C₂²×C₄	—	127	1	no	—
721	C₂²×C₄	—	127	1	no	—
722	C₂²×C₄	—	127	1	no	—
723	C₂²×C₄	—	127	1	no	—
724	C₂²×C₄	—	127	1	no	—
725	C₂²×C₄	—	127	1	no	—
726	C₂²×C₄	—	127	1	no	—
727	C₂²×C₄	—	127	1	no	—
728	C₂²×C₄	—	127	1	no	—
729	C₂²×C₄	—	508	2	no	—
730	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
733	C₄⋊C₄	—	127	1	no	—
734	C₄⋊C₄	—	127	1	no	—
735	C₄⋊C₄	—	127	1	no	—
736	C₄⋊C₄	—	127	1	no	—
737	C₄⋊C₄	—	127	1	no	—
738	C₄⋊C₄	—	127	1	no	—
739	C₄⋊C₄	—	127	1	no	—
740	C₄⋊C₄	—	127	1	no	—
741	C₄⋊C₄	—	127	1	no	—
742	C₄⋊C₄	—	127	1	no	—
743	C₄⋊C₄	—	127	1	no	—
744	C₄⋊C₄	—	127	1	no	—
745	C₄⋊C₄	—	127	1	no	—
746	C₄⋊C₄	—	127	1	no	—
747	C₄⋊C₄	—	127	1	no	—
748	C₄⋊C₄	—	127	1	no	—
749	C₄⋊C₄	—	127	1	no	—
750	C₄⋊C₄	—	127	1	no	—
751	C₄⋊C₄	—	127	1	no	—
752	C₄⋊C₄	—	127	1	no	—
753	C₄⋊C₄	—	127	1	no	—
754	C₄⋊C₄	—	127	1	no	—
755	C₄⋊C₄	—	127	1	no	—
756	C₄⋊C₄	—	127	1	no	—
757	C₄⋊C₄	—	127	1	no	—
758	C₄⋊C₄	—	127	1	no	—
759	C₄⋊C₄	—	127	1	no	—
760	C₄⋊C₄	—	127	1	no	—
761	C₄⋊C₄	—	127	1	no	—
762	C₄⋊C₄	—	127	1	no	—
763	C₄⋊C₄	—	127	1	no	—
764	C₄⋊C₄	—	127	1	no	—
765	C₄⋊C₄	—	127	1	no	—
766	C₄⋊C₄	—	127	1	no	—
767	C₄⋊C₄	—	127	1	no	—
768	C₄⋊C₄	—	127	1	no	—
769	C₄⋊C₄	—	127	1	no	—
770	C₄⋊C₄	—	127	1	no	—
771	C₄⋊C₄	—	127	1	no	—
772	C₄⋊C₄	—	127	1	no	—
773	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
783	C₂²⋊C₄	—	127	1	no	—
784	C₂²⋊C₄	—	127	1	no	—
785	C₂²⋊C₄	—	127	1	no	—
786	C₂²⋊C₄	—	127	1	no	—
787	C₂²⋊C₄	—	127	1	no	—
788	C₂²⋊C₄	—	127	1	no	—
789	C₂²⋊C₄	—	127	1	no	—
790	C₂²⋊C₄	—	127	1	no	—
791	C₂²⋊C₄	—	127	1	no	—
792	C₂²⋊C₄	—	127	1	no	—
793	C₂²⋊C₄	—	127	1	no	—
794	C₂²⋊C₄	—	127	1	no	—
795	C₂²⋊C₄	—	127	1	no	—
796	C₂²⋊C₄	—	127	1	no	—
797	C₂²⋊C₄	—	127	1	no	—
798	C₂²⋊C₄	—	127	1	no	—
799	C₂²⋊C₄	—	127	1	no	—
800	C₂²⋊C₄	—	127	1	no	—
801	C₂²⋊C₄	—	127	1	no	—
802	C₂²⋊C₄	—	127	1	no	—
803	C₂²⋊C₄	—	127	1	no	—
804	C₂²⋊C₄	—	127	1	no	—
805	C₂²⋊C₄	—	127	1	no	—
806	C₂²⋊C₄	—	127	1	no	—
807	C₂²⋊C₄	—	127	1	no	—
808	C₂²⋊C₄	—	127	1	no	—
809	C₂²⋊C₄	—	127	1	no	—
810	C₂²⋊C₄	—	127	1	no	—
811	C₂²⋊C₄	—	127	1	no	—
812	C₂²⋊C₄	—	127	1	no	—
813	C₂²⋊C₄	—	127	1	no	—
814	C₂²⋊C₄	—	127	1	no	—
815	C₂²⋊C₄	—	127	1	no	—
816	C₂²⋊C₄	—	127	1	no	—
817	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
829	C₄²	—	127	1	no	—
830	C₄²	—	127	1	no	—
831	C₄²	—	127	1	no	—
832	C₄²	—	127	1	no	—
833	C₄²	—	127	1	no	—
834	C₄²	—	127	1	no	—
835	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
836	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
837	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
838	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
839	C₂³	—	127	1	no	—
840	C₂³	—	127	1	no	—
841	C₂³	—	127	1	no	—
842	C₂³	—	127	1	no	—
843	C₂³	—	508	1	no	—
844	C₂³	—	508	1	no	—
845	C₂³	—	508	1	no	—
846	C₂³	—	254	2	no	—
847	C₂³	—	254	2	no	—
848	C₂³	—	254	2	no	—
849	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
850	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
851	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	4	1	no	—
854	Q₈	—	4	1	no	—
855	Q₈	—	508	1	no	—
856	Q₈	—	508	1	no	—
857	Q₈	—	508	1	no	—
858	Q₈	—	508	1	no	—
859	Q₈	—	508	1	no	—
860	Q₈	—	508	1	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	508	1	no	—
865	D₄	—	508	1	no	—
866	D₄	—	508	1	no	—
867	D₄	—	508	1	no	—
868	D₄	—	508	1	no	—
869	D₄	—	508	1	no	—
870	D₄	—	254	2	no	—
871	D₄	—	254	2	no	—
872	D₄	—	254	2	no	—
873	D₄	—	254	2	no	—
874	D₄	—	254	2	no	—
875	D₄	—	254	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	127	1	no	—
880	C₂×C₄	—	127	1	no	—
881	C₂×C₄	—	127	1	no	—
882	C₂×C₄	—	127	1	no	—
883	C₂×C₄	—	127	1	no	—
884	C₂×C₄	—	127	1	no	—
885	C₂×C₄	—	127	1	no	—
886	C₂×C₄	—	127	1	no	—
887	C₂×C₄	—	127	1	no	—
888	C₂×C₄	—	127	1	no	—
889	C₂×C₄	—	127	1	no	—
890	C₂×C₄	—	127	1	no	—
891	C₂×C₄	—	508	1	no	—
892	C₂×C₄	—	508	1	no	—
893	C₂×C₄	—	508	1	no	—
894	C₂×C₄	—	508	1	no	—
895	C₂×C₄	—	508	1	no	—
896	C₂×C₄	—	508	1	no	—
897	C₂×C₄	—	508	1	no	—
898	C₂×C₄	—	508	1	no	—
899	C₂×C₄	—	508	1	no	—
900	C₂×C₄	—	508	1	no	—
901	C₂×C₄	—	508	1	no	—
902	C₂×C₄	—	508	1	no	—
903	C₂×C₄	—	508	1	no	—
904	C₂×C₄	—	508	1	no	—
905	C₂×C₄	—	508	1	no	—
906	C₂×C₄	—	254	2	no	—
907	C₂×C₄	—	254	2	no	—
908	C₂×C₄	—	254	2	no	—
909	C₂×C₄	—	254	2	no	—
910	C₂×C₄	—	254	2	no	—
911	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	127	2	no	—
933	C₂²	—	127	2	no	—
934	C₂²	—	1016	2	no	—
935	C₂²	—	508	4	no	—
936	C₂²	—	254	1	no	—
937	C₂²	—	254	1	no	—
938	C₂²	—	254	1	no	—
939	C₂²	—	254	1	no	—
940	C₂²	—	254	1	no	—
941	C₂²	—	254	1	no	—
942	C₂²	—	254	1	no	—
943	C₂²	—	254	1	no	—
944	C₂²	—	254	1	no	—
945	C₂²	—	254	1	no	—
946	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	254	1	no	—
960	C₄	—	254	1	no	—
961	C₄	—	254	1	no	—
962	C₄	—	254	1	no	—
963	C₄	—	254	1	no	—
964	C₄	—	254	1	no	—
965	C₄	—	254	1	no	—
966	C₄	—	254	1	no	—
967	C₄	—	254	1	no	—
968	C₄	—	254	1	no	—
969	C₄	—	254	1	no	—
970	C₄	—	254	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	508	1	no	—
975	C₂	—	508	1	no	—
976	C₂	—	254	2	no	—
977	C₂	—	254	2	no	—
978	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
979	C₂	2₋¹⁺⁴×D₁₂₇	1	1	yes	characteristic
980	C₂	#22550712	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#542×C₁₂₇	C₂
hypercenter	#542	D₁₂₇
hypocenter	C₁₂₇	#3535
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22550628	C₂	semidirect
2. #22550626	C₂	semidirect
3. #22550621	C₂	semidirect
4. #22550620	C₂	semidirect
5. #22550586	C₂	semidirect
6. #22550580	C₂	semidirect
7. #22550567	C₂	semidirect
8. #22550565	C₂	semidirect
9. #22550556	C₂	semidirect
10. #22550554	C₂	semidirect
11. #22550551	C₂	semidirect
12. #22550550	C₂	semidirect
13. #22550528	C₂	semidirect
14. #22550524	C₂	semidirect
15. #22550519	C₂	semidirect
16. #22550515	C₂	semidirect
17. #22550503	C₂	semidirect
18. #22550501	C₂	semidirect
19. #22550496	C₂	semidirect
20. #22550472	C₂	semidirect
21. #22550469	C₂	semidirect
22. #22550468	C₂	semidirect
23. #22550467	C₂	semidirect
24. #22550467	C₂	semidirect
25. #22550460	C₂	semidirect
26. #22550451	C₂	semidirect
27. #22550446	C₂	semidirect
28. #22550385	C₂	semidirect
29. #123×D₁₂₇	C₂	semidirect
30. C₂²⋊Q₈×D₁₂₇	C₂	semidirect
31. #542×C₁₂₇	C₂	semidirect
33. C₂×#14523248	C₂²	semidirect
35. C₂×Q₈×D₁₂₇	C₂²	semidirect
38. #16861209	C₂²	semidirect
39. #16861208	C₂²	semidirect
40. #16861207	C₂²	semidirect
41. #16861207	C₂²	semidirect
42. #16861207	C₂²	semidirect
43. #16861204	C₂²	semidirect
44. #16861204	C₂²	semidirect
45. #16861203	C₂²	semidirect
46. #16861203	C₂²	semidirect
47. #16861202	C₂²	semidirect
48. #16861202	C₂²	semidirect
49. #16861202	C₂²	semidirect
50. #16861202	C₂²	semidirect
51. #16861202	C₂²	semidirect
52. #16861202	C₂²	semidirect
53. #16861201	C₂²	semidirect
54. #16861201	C₂²	semidirect
55. #16861201	C₂²	semidirect
56. #16861201	C₂²	semidirect
57. #16861200	C₂²	semidirect
58. #16861200	C₂²	semidirect
59. #16861199	C₂²	semidirect
60. #16861199	C₂²	semidirect
61. #16861199	C₂²	semidirect
62. #16861199	C₂²	semidirect
63. #16861198	C₂²	semidirect
64. #16861197	C₂²	semidirect
65. #16861196	C₂²	semidirect
67. #16861195	C₂²	semidirect
72. #16861194	C₂²	semidirect
73. #16861194	C₂²	semidirect
74. #16861194	C₂²	semidirect
76. #16861193	C₂²	semidirect
77. #16861193	C₂²	semidirect
79. #16861192	C₂²	semidirect
85. #16861191	C₂²	semidirect
86. #16861191	C₂²	semidirect
87. #16861191	C₂²	semidirect
88. #16861191	C₂²	semidirect
89. #16861191	C₂²	semidirect
90. #16861191	C₂²	semidirect
93. #16861190	C₂²	semidirect
95. #16861189	C₂²	semidirect
96. #16861189	C₂²	semidirect
97. #16861188	C₂²	semidirect
98. #16861188	C₂²	semidirect
104. #16861187	C₂²	semidirect
105. #16861187	C₂²	semidirect
106. #16861187	C₂²	semidirect
107. #16861187	C₂²	semidirect
108. #16861187	C₂²	semidirect
109. #16861187	C₂²	semidirect
110. #16861186	C₂²	semidirect
111. #16861186	C₂²	semidirect
112. #16861186	C₂²	semidirect
113. #16861186	C₂²	semidirect
114. #16861186	C₂²	semidirect
115. #16861186	C₂²	semidirect
116. #16861186	C₂²	semidirect
117. #16861186	C₂²	semidirect
118. #16861186	C₂²	semidirect
122. #16861185	C₂²	semidirect
123. #16861185	C₂²	semidirect
124. #16861185	C₂²	semidirect
129. #16861182	C₂²	semidirect
131. #16861181	C₂²	semidirect
132. #16861181	C₂²	semidirect
138. #16861174	C₂²	semidirect
143. #16861171	C₂²	semidirect
146. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
147. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
150. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
151. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
153. #16861167	C₂²	semidirect
155. #16861166	C₂²	semidirect
156. #16861166	C₂²	semidirect
157. #16861166	C₂²	semidirect
158. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
161. C₄⋊C₄×D₁₂₇	C₂²	semidirect
162. C₄⋊C₄×D₁₂₇	C₂²	semidirect
163. C₄⋊C₄×D₁₂₇	C₂²	semidirect
164. C₄⋊C₄×D₁₂₇	C₂²	semidirect
172. C₄⋊Q₈×C₁₂₇	C₂²	semidirect
173. #126×C₁₂₇	C₂²	semidirect
174. #126×C₁₂₇	C₂²	semidirect
176. #124×C₁₂₇	C₂²	semidirect
177. #124×C₁₂₇	C₂²	semidirect
179. #123×C₁₂₇	C₂²	semidirect
180. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
181. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
182. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
184. C₄×Q₈×C₁₂₇	C₂²	semidirect
185. C₄×D₄×C₁₂₇	C₂²	semidirect
186. #117×C₁₂₇	C₂²	semidirect
491. C₁₂₇	#3535	semidirect
511. #542	D₁₂₇	semidirect
534. C₄⋊Q₈	C₂×D₁₂₇	semidirect
545. #126	C₂×D₁₂₇	semidirect
546. #126	C₂×D₁₂₇	semidirect
563. #124	C₂×D₁₂₇	semidirect
564. #124	C₂×D₁₂₇	semidirect
592. #123	C₂×D₁₂₇	semidirect
624. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
625. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
626. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
642. C₄×Q₈	C₂×D₁₂₇	semidirect
656. C₄×D₄	C₂×D₁₂₇	semidirect
663. #117	C₂×D₁₂₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22550628	2
#22550626	2
#22550621	2
#22550620	2
#22550586	2
#22550580	2
#22550567	2
#22550565	2
#22550556	2
#22550554	2
#22550551	2
#22550550	2
#22550528	2
#22550524	2
#22550519	2
#22550515	2
#22550503	2
#22550501	2
#22550496	2
#22550472	2
#22550469	2
#22550468	2
#22550467	2
#22550460	2
#22550451	2
#22550446	2
#22550385	2
#123×D₁₂₇	2
C₂²⋊Q₈×D₁₂₇	2
#542×C₁₂₇	2
#3535	127